A Faster Fourier Transform

Piotr Indyk, Dina Katabi, Eric Price, and Haitham Hassanieh (left to right) have created a faster way to break down complex signals into combinations of simple waves for processing. Credit: Webb Chappell

WHOMITCambridge, Massachusetts

TECHNOLOGY
A new algorithm for processing streams of data will lead to better multimedia devices.

OTHER NOTABLE INNOVATORS

Richard BaraniukRice University, Houston, Texas

Anna Gilbert and Martin StraussUniversity of Michigan

Joel A. TroppCaltech, Pasadena, California

Mark IwenDuke University, Durham, North Carolina

In January, four MIT researchers showed off a replacement for one of the most important algorithms in computer science. Dina Katabi, Haitham Hassanieh, Piotr Indyk, and Eric Price have created a faster way to perform the Fourier transform, a mathematical technique for processing streams of data that underlies the operation of things such as digital medical imaging, Wi-Fi routers, and 4G cellular networks.

The principle of the Fourier transform, which dates back to the 19th century, is that any signal, such as a sound recording, can be represented as the sum of a collection of sine and cosine waves with different frequencies and amplitudes. This collection of waves can then be manipulated with relative ease—for example, allowing a recording to be compressed or noise to be suppressed. In the mid-1960s, a computer-friendly algorithm called the fast Fourier transform (FFT) was developed. Anyone who's marveled at the tiny size of an MP3 file compared with the same recording in an uncompressed form has seen the power of the FFT at work.

With the new algorithm, called the sparse Fourier transform (SFT), streams of data can be processed 10 to 100 times faster than was possible with the FFT. The speedup can occur because the information we care about most has a great deal of structure: music is not random noise. These meaningful signals typically have only a fraction of the possible values that a signal could take; the technical term for this is that the information is "sparse." Because the SFT algorithm isn't intended to work with all possible streams of data, it can take certain shortcuts not otherwise available. In theory, an algorithm that can handle only sparse signals is much more limited than the FFT. But "sparsity is everywhere," points out coinventor Katabi, a professor of electrical engineering and computer science. "It's in nature; it's in video signals; it's in audio signals."

A faster transform means that less computer power is required to process a given amount of information—a boon to energy-conscious mobile multimedia devices such as smart phones. Or with the same amount of power, engineers can contemplate doing things that the computing demands of the original FFT made impractical. For example, Internet backbones and routers today can actually read or process only a tiny trickle of the river of bits they pass between them. The SFT could allow researchers to study the flow of this traffic in much greater detail as bits shoot by billions of times a second.

If I had to lay a bet as to which of these 10 "technologies" will have the most effect over the next 5 years I would put my money on this one. We are talking about sending more information with less bandwidth, and many other algorithms being speeded up by this new short cut. We are living in the age of the algorithm. This is a big deal.

1066 Days Ago

04/29/2012

@ptmmac Ditto. This has immense potential, over the next 5 _and_ 50 years.

1065 Days Ago

04/30/2012

The SFT could allow the massive number of criminals in the government to study the flow of this traffic in much greater detail to extract your account details, financial information, all the better to spy on you with.

The evil ones will put this to use as soon as they can.

1057 Days Ago

05/08/2012

@GuyFalkes The SFT would only be used for Audio and Video signals, no risk for data here.

1058 Days Ago

05/07/2012

This article overstates some things. 1) mobile devices are rarely compressing... mostly decompressing (which is much easier in most cases), and 2) once you've compressed audio using something like AAC, random noise IS actually substituted for parts of the original sound.

Don't get me wrong, this is a good break through, but it's use is being overstated.

1015 Days Ago

06/19/2012

@tdistler Things are changing ...mobile devices *are* encoding content a lot more than ever before. And it's not just VOIP and Skype ...wifi Display is becoming de-facto. Content creation has been democratized, and the apps by their dozens, will surely follow.

That said, how efficient will this algorithm be for these modern apps (apps that are not necessarily dealing with professionally created content) is something to be still seen...

995 Days Ago

07/09/2012

@tdistler It seems to me sound is compressed, so is picture and video. Also radio signals. Things like touch screen, gps, motion sensor, usb probably are using. Maybe text edge smoothing/3d might also use it.

1057 Days Ago

05/08/2012

Only having a BS degree and being taught to use fourier series for solving heat transfer equations (quicker)- I'd wonder the 'pure' mathematical uses for something like this. I know that far enough along in math (bessel functions etc.) it becomes a guess at the form of the solution (2 pages to solve or ten pages depending on the guess).I'd also wonder the possible vibration theory applications- most notably persuading (for lack of a better word) resonance in systems (I like thermoacoustic devices-rijke and sondhauss, etc.).

1044 Days Ago

05/21/2012

My first job was doing FFT in hardware so we could more quickly massage and sharpen the images we were getting back from sonar signals (cold war era). I'm not sure the overall data stream was "sparse" enough to use these new algorithms but it would have at least let us pick out some of the known signatures we were trying to get rid of like whales and well known ship signatures. But we would still have used the traditional FFTs because we were always worried about those "unknowns" that those dirty commies might have surprised us with :-) Of course, it sure wouldn't have hurt to have this new SFT in our kitbag because we were trying everything to tease out signals (FFT, Laplacian, etc).

It will be interesting to see where this goes.

995 Days Ago

07/09/2012

This is awesome discovery worthy of novel prize if it can even replace 10% of fft. I can you imagine saving 90% of enegy/time/money. Things like dna can be studied cheaper. This might speed up smarter than human computer from 50 years to 25. :)

994 Days Ago

07/10/2012

One of the cofounders of the company Leap Motion came up with a set of algorithms, which were magnitudes faster than anything equivalent, for extracting distance and direction information from superpositioned diffraction data received from a CCD chip -- supposedly using an evolved form of FFT processing -- Several Years Ago. Sounds like he may have reached what appears to be the same or similar result a bit sooner than these four did. I guess that "when it's time, it happens."

952 Days Ago

08/21/2012

seems big deal

803 Days Ago

01/17/2013

Profound implications for MRI imaging where the FFT is the bedrock of providing spatial information prior to storing the signal in the imaging matrix. No FFT no MRI.

703 Days Ago

04/27/2013

Can someone show some real examples (details with the kind of image or music, the image size or the music sample and the processor or GPU that was used), so REAL benchmarks? And do you use compression in this technique? If so, I don't think it would be great for image deconvolution (since you will lose even more data in the image).

703 Days Ago

04/27/2013

Can someone show some real examples (details with the kind of image or music, the image size or the music sample and the processor or GPU that was used), so REAL benchmarks? And do you usecompression in this technique? If so, I don't think it would be great for image deconvolution (since you will lose even more data in the image).

698 Days Ago

05/02/2013

@deconv The reconstruction of a single slice from a brain MRI using a 2D 380X256x 16 bit pixel matrix compiled and spatially reconstructed by co locating a single signal point resolved from the chaotic MRI signal by phase, frequency and xy axis slice selection via fourier transform. This reply format will not allow image attachement...send me your E mail and I will send you a DICOM facsimile of a conventional brain MRI. send contact info to ted@medwise.net. We use a Siemens multichannel array processor to do the FFT and subsequent signal data deposition into an MRI "k" space array from which the gray scale image is subsequently reconstructed. Great overview of the process and role of FFT is:Horowitz: MRI Physics for Radiologists Springer - Verlag